APM  Vol.3 No.2 , March 2013
Commuting Structure Jacobi Operator for Real Hypersurfaces in Complex Space Forms
ABSTRACT

Let M be a real hypersurface of a complex space form with almost contact metric structure (φ,ξ,η,g). In this paper, we prove that if the structure Jacobi operator Rξ=,ξ) ξ is φξξ-parallel and Rξ commute with the shape operator, then M is a Hopf hypersurface. Further, if Rξ is φξξ-parallel and Rξ commute with the Ricci tensor, then M is also a Hopf hypersurface provided that TrRξ is constant.


Cite this paper
U. Ki and H. Kurihara, "Commuting Structure Jacobi Operator for Real Hypersurfaces in Complex Space Forms," Advances in Pure Mathematics, Vol. 3 No. 2, 2013, pp. 264-276. doi: 10.4236/apm.2013.32038.
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